Taiwan counterclockwise round the island 10-day tour Taoyuan-Taichung-Alishan-Kaohsiung-Kenting-Hualien-Jiufen-Pingxi Line-Taipei Is the itinerary reasonable?

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It will be very fast to play Qixingtan, Qingshui Cliff and Taroko for half a day. In addition, you need to go from 5 o'clock to Jiufen. It may be difficult to buy tickets on the railway. If you insist on taking the train, it is recommended to get on the train at Taroko Station